Using the chi-square statistic to monitor compositional process data

We investigate the use of the chi-square control chart as a simple multivariate method for shopfloor monitoring of compositional process data. Although this chart is usually considered to be applicable only with multinomial process data, we show that it is also valid, in a certain asymptotic sense, for compositional data that arise from the Dirichlet distribution. For general compositional data, we show that the chi-square statistic can be used for process monitoring, provided that we make a simple adjustment to the degrees of freedom in the chi-square reference distribution. This method is illustrated and compared in four examples with the T 2 chart based on log-ratio transformation of the data.